Least order, stable solution of the exact model matching problem

The set of all solutions of the minimal design problem (MDP) is presented in parametric form. This result is obtained by first deriving a parametric representation of all minimal bases of a particular vector space. From this the set of all solutions of the MDP are obtained. Then conditions are placed on the parameters, which conditions define the set of stable solutions of the MDP. Solutions to the nonminimal model matching problem are also presented in parametric form, and it is shown how in principle solutions of successively higher degree can be searched for a stable solution, should the MDP have no stable solution, so that a solution to the model matching problem can be found which has the lowest order consistent with a stability constraint.